Subdivision surface causes problems on connected edges (bridged edge loops)
From what i know about 3D printing, you design the object without the support and filling, no connecting of inner and outer edge-loops either, the result you got there is to be expected, subdivision does not work without artifacts if you do that.

Rather you build and design the object first as it is supposed to look, export it to the slicer software and in there you should be able to set up filling and support.

Also, thickness in the bottom should be achieved by giving the object thickness, like we usually model a vase or glass, inner and outer wall connected through the lip at the opening and the inner bottom more distant from the outer bottom, thus giving it volume.

But regarding modelling with subdivision surface modifiers, i can tell you that the problems you got there, are normal considering what you connected, as you are not supposed to use it that way.

Solution: Model normal without anything other then the model in mind, then export and add those support or filled areas in the software to prepare for the 3D print.

Regarding the infill, as i checked up now and even downloaded a slicer software just to be sure, the 3D object from Blender or any other 3D software does not need to concern itself with that. That does not mean that thin parts of the object can be filled, so giving the object a certain "hollow" thickness for the slicer software to fill is still recommended.

Here a picture of the infill options of "Slic3r" a free software:



So i would believe that most slicer software offers this as well.

I'd like to add this link as well 3D Slicer Settings, as it explains under "4. Fill Density" what i mentioned.